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Puzzling Squares - a Year 3 Investigation

By Nick Barwick - 5 Aug 2018

In Hamilton's 'Puzzling Squares' investigation, children add three single-digit numbers with the aim of making a total of 10 and understanding the impact on the sum of different constituent numbers.

Children will recall number facts to help solve the problem, relying on and consolidating number bonds to 10. They will test what happens when numbers are placed in different grid positions, working towards recognising different outcomes when odd or even numbers are placed on corners. Subsequent explanations will require some generalisations.


This learner shows how recognising and articulating a sticking-point can be a key feature of thinking mathematically. It might be a frustrating point on the journey towards solving the problem, but should be met with confidence rather than anxiety. The learner in this example was confident enough to persevere, engaging a positive, can-do mindset. Such resilience is a key skill in the problem-solver's repertoire.

Try the Puzzling Squares Investigation with your class.